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Decomposition of fuzzy soft sets with finite value spaces
Feng Feng1, Hamido Fujita2, Young Bae Jun3
1Department of Applied Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.
Thescientificworldjournal
|February 22, 2014
Summary
This study introduces decomposition theorems for fuzzy soft sets with finite value spaces. These findings enhance decision-making under uncertainty and extend classical fuzzy set decomposition theorems.
Area of Science:
- Soft computing
- Fuzzy set theory
- Decision making under uncertainty
Background:
- Fuzzy soft sets integrate gradualness and parameterization to handle uncertainty.
- Decomposition of fuzzy soft sets is crucial for theoretical and practical applications, especially in decision-making.
- Existing decomposition theorems for fuzzy sets can be extended.
Purpose of the Study:
- To explore the decomposition of fuzzy soft sets with finite value spaces.
- To introduce and investigate scalar uni-product and int-product operations for fuzzy soft sets.
- To establish decomposition theorems for fuzzy soft sets.
Main Methods:
- Introduction of scalar uni-product and int-product operations.
- Definition of t-level soft sets and level equivalent relations.
- Establishment of decomposition theorems using threshold concepts.
Main Results:
- The quotient structure of the unit interval is isomorphic to the lattice of t-level soft sets.
- Crucial threshold values and complete threshold sets are introduced.
- Decomposition theorems for fuzzy soft sets with finite value spaces are established.
Conclusions:
- The study provides novel decomposition theorems for fuzzy soft sets.
- The results generalize existing decomposition theorems for fuzzy sets.
- Applications include classification and rating, demonstrated with a cell phone example.
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